What We Cannot Know: Explorations at the Edge of Knowledge

by Marcus du Sautoy

You might ask: a wave of what? What is vibrating? In fact, it is a wave of information rather than physical stuff. Just as a crime wave isn’t a wave of criminals but rather information about the likelihood of a crime happening in a particular area. The wave is simply a mathematical function, and a mathematical function is like a machine or computer: you input information, and it calculates away and spits out an answer. The wave function of the electron has as input any region of space, and the output is the probability that you will find the electron in that region. Amazingly, this particle should really be thought of as a piece of evolving mathematics, not a physical thing at all. It is called a wave because the functions describing these probabilities have many of the features of classical wave functions. The peaks and troughs encode information about where the electron might be. The bigger the amplitude of the wave, the more likely you are to find the electron in that region of space.